context free languages

Question

State True/False:

class of context free languages are closed under union.

class of context free languages are closed under intersection.

class of context free languages are closed under complementation.

Answer 1

Class of context free languages IS closed under union.- TRUE

Class of context free languages IS closed under intersection.- FALSE

Class of context free languages IS closed under complementation.- FALSE

Class of CFLs is not closed under intersection and complementation

• intersection of 2 CFLs may or may not be a CFL - ($a^nb^nc^m \cap  a^mb^mc^n =a^nb^nc^n$ it is CSL but not NCFL )
• Complement of CFL is always CSL but may not be CFL (Complement of a DCFL is always a DCFL, but complement of NCFL may or may not be an NCFL)

Comments

yes and intersection of two DCFL can be regular too rt?

---

@srestha I have edited your answer. When you say a language belongs to a set, it automatically belongs to any of its superset and hence all properties of the superset is applicable to it.

---

yes sir , ok thank u

u r so special , whenever u do anything, it looks very beautiful to us :)